Spatial heterogeneity is important for exploring data relationships between real estate price and its influential factors. The geographically weighted regression (GWR) technique has been frequently adopted for this purpose. In this study, we collected a second-hand real estate house price data set of Wuhan, in which each property is located the same as the community it belongs to. Thus, this data set possesses a typical characteristic, that is, dozens or even hundreds of observations could be allocated to one pair of coordinates, but vary in their attributes. This specific feature might lead to serious problems with bandwidth optimisations and coefficient estimates for calibrating the GWR model. We then proposed an extension by combining the hierarchical linear model (HLM) and GWR, namely HLM-GWR to cope with these problems. Results show that the HLM-GWR performs much better than the conventional GWR and HLM technique in terms of bandwidth optimisation, coefficient estimates. With a controlled simulation test, we again validated the advantage of the HLM-GWR model in comparison to both the HLM and GWR in handling this specific scenario. Overall, HLM-GWR is workable and should be recommended in this case or other scenarios with observations of similar spatial distributions.

![HLM-GWR.jpg](/media/28060e2f-158f-4e96-847a-a314cca9af51_HLM-GWR.jpg)